Common Core State Standards for Mathematics
Grade 1
Operations and Algebraic Thinking
Add and subtract within 20.
1.OA.C.6
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Number and Operations in Base Ten
Understand place value.
1.NBT.B.2
Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
- 10 can be thought of as a bundle of ten ones — called a “ten.”
- The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
- The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
Use place value understanding and properties of operations to add and subtract.
1.NBT.C.4
Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
Grade 2
Operations and Algebraic Thinking
Add and subtract within 20.
2.OA.B.2
Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.
Number and Operations in Base Ten
Use place value understanding and properties of operations to add and subtract.
2.NBT.B.5
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Grade 3
Number and Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic.
3.NBT.A.3
Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
Ohio Mathematics Academic Content Standards (2001)
Number, Number Sense and Operations Standard
Benchmarks (K–2)
M.
Add and subtract two-digit numbers with and without regrouping.
Benchmarks (3–4)
A.
Use place value structure of the base-ten number system to read, write, represent and compare whole numbers and decimals.
Grade Level Indicators (Grade 3)
2.
Use place value concepts to represent whole numbers and decimals using numerals, words, expanded notation and physical models. For example:
a. Recognize 100 means "10 tens" as well as a single entity (1 hundred) through physical models and trading games.
b. Describe the multiplicative nature of the number system; e.g., the structure of 3205 as 3 x 1000 plus 2 x 100 plus 5 x 1.
c. Model the size of 1000 in multiple ways; e.g., packaging 1000 objects into 10 boxes of 100, modeling a meter with centimeter and decimeter strips, or gathering 1000 pop-can tabs.
d. Explain the concept of tenths and hundredths using physical models, such as metric pieces, base ten blocks, decimal squares or money.
12.
Add and subtract whole numbers with and without regrouping.
Grade Level Indicators (Grade 4)
14.
Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.
Principles and Standards for School Mathematics
Number and Operations Standard
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Expectations (3–5)
understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals;
Compute fluently and make reasonable estimates
Expectations (3–5)
understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals;
develop fluency in adding, subtracting, multiplying, and dividing whole numbers;